About Averaging in Hyperbolic Equation under the Influence of Multifrequence Disturbances

Abstract

The research deals with the existence of the
solution of the initial problem for hyperbolic equation under the
multifrequency disturbances, which are described by the system
of ordinary differential equations (ODE) with multipoint and
integral conditions. The averaging method over fast variables is
grounded and estimation of accuracy of the method which
obviously depends on the small parameter was found.